Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104765 | C2 | semidirect |
| 2. #23782236 | C2 | semidirect |
| 3. #23781848 | C2 | semidirect |
| 4. #23781843 | C2 | semidirect |
| 5. #23781682 | C2 | semidirect |
| 6. #23781649 | C2 | semidirect |
| 8. C22×Dic326 | C22 | semidirect |
| 10. #19104765 | C22 | semidirect |
| 13. C2×#14579683 | C22 | semidirect |
| 14. #19104733 | C22 | semidirect |
| 15. #19104722 | C22 | semidirect |
| 18. #19104694 | C22 | semidirect |
| 19. #19104662 | C22 | semidirect |
| 20. #19104654 | C22 | semidirect |
| 21. #19104652 | C22 | semidirect |
| 129. C163 | #3022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| #23782236 | 2 |
| #23781848 | 2 |
| #23781843 | 2 |
| #23781682 | 2 |
| #23781649 | 2 |
| #585×C163 | 2 |
| #3022 | 163 |